Finite Group Databasebeta

← #14682959

Subgroups — #14682959

Order 2816.

1406 conjugacy classes of subgroups.

The subgroup lattice has 978 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622824C211yesmaximal, characteristic
2#13066877C211yesmaximal, characteristic, complemented
3#13066876C211yesmaximal, characteristic, complemented
4#13066874C211yesmaximal, characteristic, complemented
5#13066871C211yesmaximal, characteristic, complemented
6#13066859C211yesmaximal, characteristic
7#13066859C211yesmaximal, characteristic
8#13066853C211yesmaximal, characteristic
9#13066853C211yesmaximal, characteristic
10#13066851C211yesmaximal, characteristic, complemented
11#13066847C211yesmaximal, characteristic, complemented
12#13066842C211yesmaximal, characteristic, complemented
13#13066840C211yesmaximal, characteristic, complemented
14#13066839C211yesmaximal, characteristic
15C11×C22⋊#95C211yesmaximal, characteristic
16C24×C4×C11C2211yescharacteristic
17C22×C11×C22⋊C4C2211yescharacteristic
18C22×C11×C22⋊C4C2211yescharacteristic
19C22×C22⋊Dic11C2211yescharacteristic
20C22×C22⋊Dic11C2211yescharacteristic
21C22×C22⋊Dic11C2211yescharacteristic
22C22×C22⋊Dic11C2211yescharacteristic
23C22×Dic11⋊C4C2211yescharacteristic
24C22×Dic11⋊C4C2211yescharacteristic
25C22×C4×Dic11C2211yescharacteristic
26C22×C4×Dic11C2211yescharacteristic
27C2×C11×#95C2211yescharacteristic
28C2×C11×#95C2211yescharacteristic
29C2×C11×#95C2211yescharacteristic
30C2×C11×#95C2211yescharacteristic
31#10622824C418yescomplemented
32C2×C11⋊#95C2211yescharacteristic
33C2×C11⋊#95C2211yescharacteristic
34C2×C11⋊#95C2211yescharacteristic
35C2×C11⋊#95C2211yescharacteristic
36C2×C11⋊#95C2211yescharacteristic
37C2×C11⋊#95C2211yescharacteristic
38C2×C11⋊#95C2211yescharacteristic
39C2×C11⋊#95C2211yescharacteristic
40C2×C11⋊#95C2211yescharacteristic
41C2×C11⋊#95C2211yescharacteristic
42C2×C11⋊#95C2211yescharacteristic
43C2×C11⋊#95C2211yescharacteristic
44C2×C11⋊#95C2211yescharacteristic
45C2×C11⋊#95C2211yescharacteristic
46C2×C11⋊#95C2211yescharacteristic
47C2×C11⋊#95C2211yescharacteristic
48C2×C11⋊#95C2211yescharacteristic
49C2×C11⋊#95C2211yescharacteristic
50C2×C11⋊#95C2211yescharacteristic
51C2×C11⋊#95C2211yescharacteristic
52C25×C11C2311yescharacteristic
53C23×C4×C11—22no—
54C23×C4×C11—22no—
55C23×C4×C11—41no—
56C23×C4×C11—41no—
57C23×C4×C11—41no—
58C23×C4×C11—41no—
59C23×C4×C11C2×C414yes—
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C23×Dic11C2311yescharacteristic
67C23×Dic11C2311yescharacteristic
68C23×Dic11C2311yescharacteristic
69C23×Dic11C2311yescharacteristic
70C23×Dic11C2311yescharacteristic
71C23×Dic11C2311yescharacteristic
72C23×Dic11C2311yescharacteristic
73C23×Dic11C2311yescharacteristic
74C2×C11×C22⋊C4—22no—
75C2×C11×C22⋊C4—22no—
76C2×C11×C22⋊C4—22no—
77C2×C11×C22⋊C4—22no—
78C2×C11×C22⋊C4—41no—
79C2×C11×C22⋊C4—41no—
80C2×C22⋊Dic11—22no—
81C2×C22⋊Dic11—22no—
82C2×C22⋊Dic11—22no—
83C2×C22⋊Dic11—22no—
84C2×C22⋊Dic11—41no—
85C2×C22⋊Dic11—41no—
86C2×C22⋊Dic11—41no—
87C2×C22⋊Dic11—41no—
88C2×C22⋊Dic11—41no—
89C2×C22⋊Dic11—41no—
90C2×C22⋊Dic11C2×C414yes—
91C2×C22⋊Dic11C2×C414yes—
92C2×Dic11⋊C4—22no—
93C2×Dic11⋊C4—22no—
94C2×Dic11⋊C4—41no—
95C2×Dic11⋊C4—41no—
96C2×Dic11⋊C4—41no—
97C2×Dic11⋊C4—41no—
98C2×C4×Dic11—22no—
99C2×C4×Dic11—22no—
100C2×C4×Dic11—41no—
101C2×C4×Dic11—41no—
102C2×C4×Dic11—41no—
103C2×C4×Dic11—41no—
104C11×#95—41no—
105C11×#95—41no—
106C11×#95—41no—
107C11×#95—41no—
108C11⋊#95—22no—
109C11⋊#95—22no—
110C11⋊#95—22no—
111C11⋊#95—22no—
112C11⋊#95—41no—
113C11⋊#95—41no—
114C11⋊#95—41no—
115C11⋊#95—41no—
116C11⋊#95—41no—
117C11⋊#95—41no—
118C11⋊#95—41no—
119C11⋊#95—41no—
120C11⋊#95—41no—
121C11⋊#95—41no—
122C11⋊#95—41no—
123C11⋊#95—41no—
124C11⋊#95C2×C414yes—
125C11⋊#95C2×C414yes—
126C11⋊#95C2×C414yes—
127C11⋊#95C2×C414yes—
128#14507—111nomaximal, Sylow
129C24×C11—21no—
130C24×C11—21no—
131C24×C11—21no—
132C24×C11—21no—
133C24×C11—21no—
134C24×C11—21no—
135C24×C11—21no—
136C24×C11—21no—
137C24×C11—21no—
138C24×C11—21no—
139C24×C11—21no—
140C24×C11—21no—
141C24×C11C22×C412yes—
142C24×C11#4112yes—
143C24×C11#4112yes—
144C24×C11C2411yescharacteristic
145C22×C4×C11—28no—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11—21no—
162C22×C4×C11—21no—
163C22×C4×C11—21no—
164C22×C4×C11—21no—
165C22×C4×C11—21no—
166C22×C4×C11—21no—
167C22×C4×C11—21no—
168C22×C4×C11—21no—
169C22×C4×C11—21no—
170C22×C4×C11—21no—
171C22×C4×C11—21no—
172C22×C4×C11—21no—
173C22×C4×C11—21no—
174C22×C4×C11—21no—
175C22×C4×C11—21no—
176C22×C4×C11—21no—
177C22×C4×C11—21no—
178C22×C4×C11—21no—
179C22×C4×C11—21no—
180C22×C4×C11—21no—
181C22×C4×C11—21no—
182C22×C4×C11—21no—
183C22×C4×C11—21no—
184C22×C4×C11—44no—
185C22×C4×C11—44no—
186C22×C4×C11—44no—
187C22×C4×C11—44no—
188C22×C4×C11—44no—
189C22×C4×C11—44no—
190C22×C4×C11C22×C412yes—
191C22×C4×C11C22×C412yes—
192C22×C4×C11#4112yes—
193C22×C4×C11#4112yes—
194C22×Dic11—21no—
195C22×Dic11—21no—
196C22×Dic11—21no—
197C22×Dic11—21no—
198C22×Dic11—21no—
199C22×Dic11—21no—
200C22×Dic11—21no—
201C22×Dic11—21no—
202C22×Dic11—21no—
203C22×Dic11—21no—
204C22×Dic11—21no—
205C22×Dic11—21no—
206C22×Dic11—21no—
207C22×Dic11—21no—
208C22×Dic11—21no—
209C22×Dic11—21no—
210C22×Dic11—21no—
211C22×Dic11—21no—
212C22×Dic11—21no—
213C22×Dic11—21no—
214C22×Dic11—21no—
215C22×Dic11—21no—
216C22×Dic11—21no—
217C22×Dic11—21no—
218C22×Dic11—21no—
219C22×Dic11—21no—
220C22×Dic11—21no—
221C22×Dic11—21no—
222C22×Dic11—21no—
223C22×Dic11—21no—
224C22×Dic11—21no—
225C22×Dic11—21no—
226C22×Dic11—21no—
227C22×Dic11—21no—
228C22×Dic11—21no—
229C22×Dic11—21no—
230C22×Dic11—21no—
231C22×Dic11—21no—
232C22×Dic11—21no—
233C22×Dic11—21no—
234C22×Dic11—21no—
235C22×Dic11—21no—
236C22×Dic11—21no—
237C22×Dic11—21no—
238C22×Dic11—21no—
239C22×Dic11—21no—
240C22×Dic11—21no—
241C22×Dic11—21no—
242C22×Dic11—21no—
243C22×Dic11—21no—
244C22×Dic11C22×C412yes—
245C22×Dic11C22×C412yes—
246C22×Dic11C22×C412yes—
247C22×Dic11C22×C412yes—
248C22×Dic11#4112yes—
249C22×Dic11#4112yes—
250C11×C22⋊C4—44no—
251C11×C22⋊C4—44no—
252C22⋊Dic11—44no—
253C22⋊Dic11—44no—
254C22⋊Dic11—44no—
255C22⋊Dic11—44no—
256Dic11⋊C4—44no—
257Dic11⋊C4—44no—
258C4×Dic11—44no—
259C4×Dic11—44no—
260C2×#381—111no—
261#1443—111no—
262#1443—111no—
263#1442—111no—
264#1442—111no—
265#1439—111no—
266#1439—111no—
267#1437—111no—
268#1437—111no—
269#1436—111no—
270#1436—111no—
271#1434—111no—
272#1434—111no—
273C22⋊#95—111no—
274C22⋊#95D1111yescharacteristic
275C23×C11—22no—
276C23×C11—22no—
277C23×C11—22no—
278C23×C11—22no—
279C23×C11—22no—
280C23×C11—22no—
281C23×C11—22no—
282C23×C11—22no—
283C23×C11—22no—
284C23×C11—22no—
285C23×C11—22no—
286C23×C11—22no—
287C23×C11—22no—
288C23×C11—22no—
289C23×C11—22no—
290C23×C11—22no—
291C23×C11—22no—
292C23×C11—22no—
293C23×C11—41no—
294C23×C11—41no—
295C23×C11—41no—
296C23×C11—41no—
297C23×C11—41no—
298C23×C11—41no—
299C23×C11—41no—
300C23×C11—41no—
301C23×C11—41no—
302C23×C11—41no—
303C23×C11—41no—
304C23×C11—41no—
305C23×C11—41no—
306C23×C11—41no—
307C23×C11—41no—
308C23×C11—41no—
309C23×C11#11714yes—
310C23×C11C23×C411yescharacteristic
311C23×C11C2×#4111yescharacteristic
312C23×C11C2×#4111yescharacteristic
313C23×C11C2×#4111yescharacteristic
314C23×C11C2×#4111yescharacteristic
315C23×C11C2×#4111yescharacteristic
316C23×C11C2×#4111yescharacteristic
317C23×C11H(5,𝔽2)11yescharacteristic
318C23×C11H(5,𝔽2)11yescharacteristic
319C23×C11H(5,𝔽2)11yescharacteristic
320C23×C11H(5,𝔽2)11yescharacteristic
321C23×C11H(5,𝔽2)11yescharacteristic
322C23×C11H(5,𝔽2)11yescharacteristic
323C23×C112−1+411yescharacteristic
324C23×C112−1+411yescharacteristic
325C2×C4×C11—22no—
326C2×C4×C11—22no—
327C2×C4×C11—22no—
328C2×C4×C11—22no—
329C2×C4×C11—22no—
330C2×C4×C11—22no—
331C2×C4×C11—22no—
332C2×C4×C11—22no—
333C2×C4×C11—22no—
334C2×C4×C11—22no—
335C2×C4×C11—22no—
336C2×C4×C11—22no—
337C2×C4×C11—416no—
338C2×C4×C11—41no—
339C2×C4×C11—41no—
340C2×C4×C11—41no—
341C2×C4×C11—41no—
342C2×C4×C11—41no—
343C2×C4×C11—41no—
344C2×C4×C11—41no—
345C2×C4×C11—41no—
346C2×C4×C11—41no—
347C2×C4×C11—41no—
348C2×C4×C11—41no—
349C2×C4×C11—41no—
350C2×C4×C11—41no—
351C2×C4×C11—41no—
352C2×C4×C11—41no—
353C2×C4×C11—41no—
354C2×C4×C11—41no—
355C2×C4×C11—41no—
356C2×C4×C11—41no—
357C2×C4×C11—41no—
358C2×C4×C11—41no—
359C2×C4×C11—41no—
360C2×C4×C11—41no—
361C2×C4×C11—41no—
362C2×C4×C11—41no—
363C2×C4×C11—41no—
364C2×C4×C11—41no—
365C2×C4×C11—41no—
366C2×C4×C11—41no—
367C2×C4×C11—41no—
368C2×Dic11—22no—
369C2×Dic11—22no—
370C2×Dic11—22no—
371C2×Dic11—22no—
372C2×Dic11—22no—
373C2×Dic11—22no—
374C2×Dic11—22no—
375C2×Dic11—22no—
376C2×Dic11—22no—
377C2×Dic11—22no—
378C2×Dic11—22no—
379C2×Dic11—22no—
380C2×Dic11—22no—
381C2×Dic11—22no—
382C2×Dic11—22no—
383C2×Dic11—22no—
384C2×Dic11—22no—
385C2×Dic11—22no—
386C2×Dic11—41no—
387C2×Dic11—41no—
388C2×Dic11—41no—
389C2×Dic11—41no—
390C2×Dic11—41no—
391C2×Dic11—41no—
392C2×Dic11—41no—
393C2×Dic11—41no—
394C2×Dic11—41no—
395C2×Dic11—41no—
396C2×Dic11—41no—
397C2×Dic11—41no—
398C2×Dic11—41no—
399C2×Dic11—41no—
400C2×Dic11—41no—
401C2×Dic11—41no—
402C2×Dic11—41no—
403C2×Dic11—41no—
404C2×Dic11—41no—
405C2×Dic11—41no—
406C2×Dic11—41no—
407C2×Dic11—41no—
408C2×Dic11—41no—
409C2×Dic11—41no—
410C2×Dic11—41no—
411C2×Dic11—41no—
412C2×Dic11—41no—
413C2×Dic11—41no—
414C2×Dic11—41no—
415C2×Dic11—41no—
416C2×Dic11—41no—
417C2×Dic11—41no—
418C2×Dic11—41no—
419C2×Dic11—41no—
420C2×Dic11—41no—
421C2×Dic11—41no—
422C2×Dic11—41no—
423C2×Dic11—41no—
424C24×C4C2×D1111yescharacteristic
425C22×C4⋊C4—111no—
426C22×C4⋊C4—111no—
427C22×C22⋊C4—111no—
428C22×C22⋊C4—111no—
429C22×C22⋊C4—111no—
430C22×C22⋊C4—111no—
431C22×C22⋊C4C2×D1111yescharacteristic
432C22×C22⋊C4C2×D1111yescharacteristic
433C22×C42—111no—
434C22×C42—111no—
435#381—118no—
436C2×#95—111no—
437C2×#95—111no—
438C2×#95—111no—
439C2×#95—111no—
440C2×#95—111no—
441C2×#95—111no—
442C2×#95—111no—
443C2×#95—111no—
444C2×#95—111no—
445C2×#95—111no—
446C2×#95—111no—
447C2×#95—111no—
448C2×#95—111no—
449C2×#95—111no—
450C2×#95—111no—
451C2×#95—111no—
452C2×#95—111no—
453C2×#95—111no—
454C2×#95—111no—
455C2×#95—111no—
456C2×#95C2×D1111yescharacteristic
457C2×#95C2×D1111yescharacteristic
458C2×#95C2×D1111yescharacteristic
459C2×#95C2×D1111yescharacteristic
460C22×C11—24no—
461C22×C11—24no—
462C22×C11—24no—
463C22×C11—42no—
464C22×C11—42no—
465C22×C11—42no—
466C22×C11—42no—
467C22×C11—42no—
468C22×C11—42no—
469C22×C11—42no—
470C22×C11—42no—
471C22×C11—42no—
472C22×C11—42no—
473C22×C11—42no—
474C22×C11—42no—
475C22×C11C2×#11711yescharacteristic
476C22×C11C4×#4111yescharacteristic
477C22×C11C4×#4111yescharacteristic
478C22×C11#51811yescharacteristic
479C22×C11#51811yescharacteristic
480C22×C11#52011yescharacteristic
481C22×C11#52011yescharacteristic
482C22×C11#53811yescharacteristic
483C22×C11#53811yescharacteristic
484C22×C11#53811yescharacteristic
485C22×C11#53811yescharacteristic
486C22×C11#53811yescharacteristic
487C22×C11#53811yescharacteristic
488C22×C11#53911yescharacteristic
489C22×C11#53911yescharacteristic
490C22×C11#54011yescharacteristic
491C22×C11#54011yescharacteristic
492C22×C11#54211yescharacteristic
493C22×C11#54211yescharacteristic
494C22×C11#55111yescharacteristic
495C22×C11#55111yescharacteristic
496C22×C11#55111yescharacteristic
497C22×C11#55111yescharacteristic
498C22×C11#55111yescharacteristic
499C22×C11#55211yescharacteristic
500C22×C11#55211yescharacteristic
501C22×C11#55211yescharacteristic
502C22×C11#55211yescharacteristic
503C22×C11#55311yescharacteristic
504C22×C11#55311yescharacteristic
505C22×C11#55911yescharacteristic
506C22×C11#56011yescharacteristic
507C22×C11#56211yescharacteristic
508C22×C11#56211yescharacteristic
509C22×C11#56311yescharacteristic
510C4×C11—42no—
511C4×C11—42no—
512C4×C11—42no—
513C4×C11—42no—
514C4×C11—81no—
515C4×C11—81no—
516Dic11—42no—
517Dic11—42no—
518Dic11—42no—
519Dic11—42no—
520Dic11—42no—
521Dic11—42no—
522Dic11—81no—
523Dic11—81no—
524C25C22×D1111yescharacteristic
525C23×C4—22no—
526C23×C4—22no—
527C23×C4—41no—
528C23×C4—41no—
529C23×C4—41no—
530C23×C4—41no—
531C23×C4—111no—
532C23×C4—111no—
533C23×C4—111no—
534C23×C4—111no—
535C23×C4—111no—
536C23×C4—111no—
537C23×C4—111no—
538C23×C4—111no—
539C23×C4C4×D1114yes—
540C23×C4C22×D1111yescharacteristic
541C23×C4C22×D1111yescharacteristic
542C23×C4C22×D1111yescharacteristic
543C23×C4C22×D1111yescharacteristic
544C23×C4C22×D1111yescharacteristic
545C23×C4C22×D1111yescharacteristic
546C2×C4⋊C4—222no—
547C2×C4⋊C4—222no—
548C2×C4⋊C4—441no—
549C2×C4⋊C4—441no—
550C2×C4⋊C4—441no—
551C2×C4⋊C4—441no—
552C2×C22⋊C4—22no—
553C2×C22⋊C4—22no—
554C2×C22⋊C4—22no—
555C2×C22⋊C4—22no—
556C2×C22⋊C4—41no—
557C2×C22⋊C4—41no—
558C2×C22⋊C4—114no—
559C2×C22⋊C4—114no—
560C2×C22⋊C4—222no—
561C2×C22⋊C4—222no—
562C2×C22⋊C4—222no—
563C2×C22⋊C4—222no—
564C2×C22⋊C4—441no—
565C2×C22⋊C4—441no—
566C2×C22⋊C4—441no—
567C2×C22⋊C4—441no—
568C2×C22⋊C4—441no—
569C2×C22⋊C4—441no—
570C2×C42—222no—
571C2×C42—222no—
572C2×C42—441no—
573C2×C42—441no—
574C2×C42—441no—
575C2×C42—441no—
576#95—41no—
577#95—41no—
578#95—41no—
579#95—41no—
580#95—114no—
581#95—114no—
582#95—114no—
583#95—114no—
584#95—222no—
585#95—222no—
586#95—222no—
587#95—222no—
588#95—441no—
589#95—441no—
590#95—441no—
591#95—441no—
592#95—441no—
593#95—441no—
594#95—441no—
595#95—441no—
596#95—441no—
597#95—441no—
598#95—441no—
599#95—441no—
600C2×C11—44no—
601C2×C11#231211yescharacteristic
602C2×C11#233511yescharacteristic
603C2×C11#233511yescharacteristic
604C2×C11#234311yescharacteristic
605C2×C11#234311yescharacteristic
606C2×C11#237411yescharacteristic
607C2×C11#237611yescharacteristic
608C2×C11#274311yescharacteristic
609C2×C11#274311yescharacteristic
610C2×C11#274911yescharacteristic
611C2×C11#274911yescharacteristic
612C2×C11#275111yescharacteristic
613C2×C11#275111yescharacteristic
614C2×C11#276511yescharacteristic
615C2×C11#276511yescharacteristic
616C24—21no—
617C24—21no—
618C24—21no—
619C24—21no—
620C24—21no—
621C24—21no—
622C24—21no—
623C24—21no—
624C24—21no—
625C24—21no—
626C24—21no—
627C24—21no—
628C24C2×C4×D1112yes—
629C24#434112yes—
630C24#434112yes—
631C24C23×D1111yescharacteristic
632C22×C4—28no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—44no—
672C22×C4—44no—
673C22×C4—44no—
674C22×C4—44no—
675C22×C4—44no—
676C22×C4—44no—
677C22×C4—112no—
678C22×C4—112no—
679C22×C4—112no—
680C22×C4—112no—
681C22×C4—112no—
682C22×C4—112no—
683C22×C4—221no—
684C22×C4—221no—
685C22×C4—221no—
686C22×C4—221no—
687C22×C4—221no—
688C22×C4—221no—
689C22×C4—221no—
690C22×C4—221no—
691C22×C4—221no—
692C22×C4—221no—
693C22×C4—221no—
694C22×C4—221no—
695C22×C4—221no—
696C22×C4—221no—
697C22×C4—221no—
698C22×C4—221no—
699C22×C4—221no—
700C22×C4—221no—
701C22×C4—221no—
702C22×C4—221no—
703C22×C4—221no—
704C22×C4—221no—
705C22×C4—221no—
706C22×C4—221no—
707C22×C4—221no—
708C22×C4—221no—
709C22×C4—221no—
710C22×C4—221no—
711C22×C4—221no—
712C22×C4—221no—
713C22×C4—221no—
714C22×C4—221no—
715C22×C4—221no—
716C22×C4—221no—
717C22×C4—221no—
718C22×C4—221no—
719C22×C4—221no—
720C22×C4—221no—
721C22×C4—221no—
722C22×C4—221no—
723C22×C4—221no—
724C22×C4—221no—
725C22×C4—221no—
726C22×C4—221no—
727C22×C4—221no—
728C22×C4—221no—
729C22×C4—221no—
730C22×C4—221no—
731C22×C4—221no—
732C22×C4—221no—
733C22×C4C2×C4×D1112yes—
734C22×C4C2×C4×D1112yes—
735C22×C4#433912yes—
736C22×C4#433912yes—
737C4⋊C4—444no—
738C4⋊C4—444no—
739C22⋊C4—44no—
740C22⋊C4—44no—
741C22⋊C4—444no—
742C22⋊C4—444no—
743C22⋊C4—444no—
744C22⋊C4—444no—
745C42—444no—
746C42—444no—
747C11#1450711yescharacteristic, complemented, Sylow
748C23—22no—
749C23—22no—
750C23—22no—
751C23—22no—
752C23—22no—
753C23—22no—
754C23—22no—
755C23—22no—
756C23—22no—
757C23—22no—
758C23—22no—
759C23—22no—
760C23—22no—
761C23—22no—
762C23—22no—
763C23—22no—
764C23—22no—
765C23—22no—
766C23—41no—
767C23—41no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23—41no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23#6693014yes—
783C23C22×C4×D1111yescharacteristic
784C23C2×#433911yescharacteristic
785C23C2×#433911yescharacteristic
786C23C2×#434111yescharacteristic
787C23C2×#434111yescharacteristic
788C23#6703711yescharacteristic
789C23#6703711yescharacteristic
790C23#6703711yescharacteristic
791C23#6703711yescharacteristic
792C23#6703711yescharacteristic
793C23#6704011yescharacteristic
794C23#41×D1111yescharacteristic
795C23#41×D1111yescharacteristic
796C23#6704211yescharacteristic
797C23#6704311yescharacteristic
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—416no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—222no—
842C2×C4—222no—
843C2×C4—222no—
844C2×C4—222no—
845C2×C4—222no—
846C2×C4—222no—
847C2×C4—222no—
848C2×C4—222no—
849C2×C4—222no—
850C2×C4—222no—
851C2×C4—222no—
852C2×C4—222no—
853C2×C4—222no—
854C2×C4—222no—
855C2×C4—222no—
856C2×C4—222no—
857C2×C4—222no—
858C2×C4—222no—
859C2×C4—441no—
860C2×C4—441no—
861C2×C4—441no—
862C2×C4—441no—
863C2×C4—441no—
864C2×C4—441no—
865C2×C4—441no—
866C2×C4—441no—
867C2×C4—441no—
868C2×C4—441no—
869C2×C4—441no—
870C2×C4—441no—
871C2×C4—441no—
872C2×C4—441no—
873C2×C4—441no—
874C2×C4—441no—
875C2×C4—441no—
876C2×C4—441no—
877C2×C4—441no—
878C2×C4—441no—
879C2×C4—441no—
880C2×C4—441no—
881C2×C4—441no—
882C2×C4—441no—
883C2×C4—441no—
884C2×C4—441no—
885C2×C4—441no—
886C2×C4—441no—
887C2×C4—441no—
888C2×C4—441no—
889C2×C4—441no—
890C2×C4—441no—
891C2×C4—441no—
892C2×C4—441no—
893C2×C4—441no—
894C2×C4—441no—
895C2×C4—441no—
896C2×C4—441no—
897C22—24no—
898C22—24no—
899C22—24no—
900C22—42no—
901C22—42no—
902C22—42no—
903C22—42no—
904C22—42no—
905C22—42no—
906C22—42no—
907C22—42no—
908C22—42no—
909C22—42no—
910C22—42no—
911C22—42no—
912C22C4×#433911yescharacteristic
913C22C2×#6693011yescharacteristic
914C22#1062301711yescharacteristic
915C22#1062301711yescharacteristic
916C22#1062302611yescharacteristic
917C22#1062302611yescharacteristic
918C22#1062303511yescharacteristic
919C22#1062304411yescharacteristic
920C22#1062304411yescharacteristic
921C22#1062305311yescharacteristic
922C22#1062305411yescharacteristic
923C22#1062307111yescharacteristic
924C22#1062308711yescharacteristic
925C22#1062308911yescharacteristic
926C22#1062309011yescharacteristic
927C22#1062309111yescharacteristic
928C22#1062309211yescharacteristic
929C22#1062309311yescharacteristic
930C22#1062309511yescharacteristic
931C22#1062312411yescharacteristic
932C22#1062312411yescharacteristic
933C22#1062312411yescharacteristic
934C22#1062312411yescharacteristic
935C22#1062314411yescharacteristic
936C22#1062314611yescharacteristic
937C22#1062315111yescharacteristic
938C22#1062315211yescharacteristic
939C22#1062316911yescharacteristic
940C22#1062317111yescharacteristic
941C22#1062317711yescharacteristic
942C22#1062317811yescharacteristic
943C22#1062318111yescharacteristic
944C22#1062318111yescharacteristic
945C22#1062318911yescharacteristic
946C22#1062318911yescharacteristic
947C4—42no—
948C4—42no—
949C4—42no—
950C4—42no—
951C4—81no—
952C4—81no—
953C4—442no—
954C4—442no—
955C4—442no—
956C4—442no—
957C4—442no—
958C4—442no—
959C4—881no—
960C4—881no—
961C2—44no—
962C2#1307121211yescharacteristic
963C2#1307140211yescharacteristic
964C2#1307140611yescharacteristic
965C2#1307147211yescharacteristic
966C2#1307147811yescharacteristic
967C2#1307174711yescharacteristic
968C2#1307176011yescharacteristic
969C2#1307575011yescharacteristic
970C2#1307575311yescharacteristic
971C2#1307583911yescharacteristic
972C2#1307584311yescharacteristic
973C2#1307586911yescharacteristic
974C2#1307587311yescharacteristic
975C2#1307605111yescharacteristic
976C2#1307605511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×C22⋊#95C2
socle, cosocleC24×C11C24
prime radicalC25×C11C23
hypercenterC22⋊#95D11
hypocenterC11#14507
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #13066877C2semidirect
3. #13066876C2semidirect
4. #13066874C2semidirect
5. #13066871C2semidirect
10. #13066851C2semidirect
11. #13066847C2semidirect
12. #13066842C2semidirect
13. #13066840C2semidirect
31. #10622824C4semidirect
747. C11#14507semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#106228242
#130668772
#130668762
#130668742
#130668712
#130668592
#130668532
#130668512
#130668472
#130668422
#130668402
#130668392
C11×C22⋊#952
#1450711